All Combinations

Problem Link

Problem

Implement type AllCombinations<S> that return all combinations of strings which use characters from S at most once.

type AllCombinations_ABC = AllCombinations<'ABC'>
// should be '' | 'A' | 'B' | 'C' | 'AB' | 'AC' | 'BA' | 'BC' | 'CA' | 'CB' | 'ABC' | 'ACB' | 'BAC' | 'BCA' | 'CAB' | 'CBA'

Solution

Approach: Union-Based Permutation

First convert the string to a union of individual characters, then build all permutations recursively.

// Convert string to union of characters
type StringToUnion<S extends string> =
  S extends `${infer C}${infer Rest}` ? C | StringToUnion<Rest> : never

// Generate all combinations (each char used at most once)
type AllCombinations<
  S extends string,
  U extends string = StringToUnion<S>
> = [U] extends [never]
  ? ''
  : '' | {
      [C in U]: `${C}${AllCombinations<never, Exclude<U, C>>}`
    }[U]

How it works:

1. StringToUnion converts 'ABC' → 'A' | 'B' | 'C'.
2. For each character C in union U, we prepend C to every combination built from the remaining characters Exclude<U, C>.
3. We always include '' (empty string) as a valid combination.
4. The mapped type { [C in U]: ... }[U] distributes over all union members.

Key Takeaways

• Exclude<U, C> removes a specific member from a union — essential for "use each item at most once" problems.
• Distributing over a union with { [K in U]: ... }[U] is the type-level equivalent of Array.flatMap.
• Including '' in the base case ensures the empty combination is always valid.